I start with assuming a gravitational scalar field as the dark-energy supposed to be responsible for the accelerating universe. Also from the point of view of unification, a scalar field implies a time-variability of certain “constants” in Nature. In this context I once derived a relation for the time-variability of the fine-structure constant α: Δα/α =ζ Ƶ(α/π) Δσ, where ζ and Ƶ are the constants of the order one, while σ on the right-hand side is the scalar field in action in the accelerating universe. I use the reduced Planckian units with c=ℏ =MP(=(8π G)−1/2)=1. I then compared the dynamics of the accelerating universe, on one hand, and Δα/α derived from the analyses of QSO absorption lines, Oklo phenomenon, also different atomic clocks in the laboratories, on the other hand. I am here going to discuss the theoretical background of the relation, based on the scalar-tensor theory invented first by Jordan in 1955.